I replaced a light fixture, no problem with light just that it was old. After replacing the light would not turn off. I checked the connections and eerything looked all right. Upon checking. I disconnected the switch, remoed the light. I connected just the black wire from the switch to the power. With switch out I had power on the black wire and also the white wire which was disconnected from the swith and also from the junction box. I thought there might be a short somewhere in the cable so I replaced the cable. Once cable was replaced I hooked everything up and have the same problem. Any help would be greatly appricated.

Sounds like you have a switch loop. In the ceiling box identify the wires coming from the switch and separate them. Turn the switch off. Connect the ceiling box white to the light white. Connect the hot black to the switch white and the switch black to the light black. Put black tape on the white wires conducting power.Try that and let us know how that works.